Geometries and Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course |
| Beschreibung: | 1 Online-Ressource (VIII, 251p. 159 illus) |
| ISBN: | 9783642615702 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-61570-2 |
Internformat
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| 300 | |a 1 Online-Ressource (VIII, 251p. 159 illus) | ||
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| 500 | |a This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Topology | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Nikulin, Viacheslav V. |
| author_facet | Nikulin, Viacheslav V. |
| author_role | aut |
| author_sort | Nikulin, Viacheslav V. |
| author_variant | v v n vv vvn |
| building | Verbundindex |
| bvnumber | BV042422807 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879624009 (DE-599)BVBBV042422807 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-61570-2 |
| format | Electronic eBook |
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| id | DE-604.BV042422807 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642615702 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858224 |
| oclc_num | 879624009 |
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| physical | 1 Online-Ressource (VIII, 251p. 159 illus) |
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| publishDate | 1994 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Nikulin, Viacheslav V. Verfasser aut Geometries and Groups by Viacheslav V. Nikulin, Igor R. Shafarevich Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (VIII, 251p. 159 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 This book is devoted to the theory of geometries which are locally Euclidean, in the sense that in small regions they are identical to the geometry of the Euclidean plane or Euclidean 3-space. Starting from the simplest examples, we proceed to develop a general theory of such geometries, based on their relation with discrete groups of motions of the Euclidean plane or 3-space; we also consider the relation between discrete groups of motions and crystallography. The description of locally Euclidean geometries of one type shows that these geometries are themselves naturally represented as the points of a new geometry. The systematic study of this new geometry leads us to 2-dimensional Lobachevsky geometry (also called non-Euclidean or hyperbolic geometry) which, following the logic of our study, is constructed starting from the properties of its group of motions. Thus in this book we would like to introduce the reader to a theory of geometries which are different from the usual Euclidean geometry of the plane and 3-space, in terms of examples which are accessible to a concrete and intuitive study. The basic method of study is the use of groups of motions, both discrete groups and the groups of motions of geometries. The book does not presuppose on the part of the reader any preliminary knowledge outside the limits of a school geometry course Mathematics Group theory Geometry Topology Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Geometrie (DE-588)4020236-7 s 1\p DE-604 Shafarevich, Igor R. Sonstige oth Erscheint auch als 978-3-540-15281-1 Druck-Ausgabe https://doi.org/10.1007/978-3-642-61570-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nikulin, Viacheslav V. Geometries and Groups Mathematics Group theory Geometry Topology Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4072157-7 |
| title | Geometries and Groups |
| title_auth | Geometries and Groups |
| title_exact_search | Geometries and Groups |
| title_full | Geometries and Groups by Viacheslav V. Nikulin, Igor R. Shafarevich |
| title_fullStr | Geometries and Groups by Viacheslav V. Nikulin, Igor R. Shafarevich |
| title_full_unstemmed | Geometries and Groups by Viacheslav V. Nikulin, Igor R. Shafarevich |
| title_short | Geometries and Groups |
| title_sort | geometries and groups |
| topic | Mathematics Group theory Geometry Topology Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Mathematics Group theory Geometry Topology Group Theory and Generalizations Mathematik Geometrie Gruppentheorie |
| url | https://doi.org/10.1007/978-3-642-61570-2 |
| work_keys_str_mv | AT nikulinviacheslavv geometriesandgroups AT shafarevichigorr geometriesandgroups |